Some highlights:
As previously surmised, M!Robin and F!Robin's combat intro are exactly the same.
M!Robin shows off his C5, but the finisher is actually different this time. Instead of a big lightning ball, he conjures pillars of light to strike the ground instead. Though, it could be his C6.
Frederick's Axe glows with a green light during his finishing blow in his Musou ttack. Due to that, it's highly likely that his element is Wind.
Robin's critical hit is shown during Female Robin's segment: lots of fire explosions before a flare of light.
What appears to be Lissa's Awakening Musou is shown.
So... for known elemental users:
Fire: Camilla
Thunder: Chrom, Lissa, Lucina, Ryoma
Wind: Frederick, Takumi
Light: Rowan, Lianna, Marth, Cordelia, Hinoka
Dark: Corrin, Xander
All: Robin, Leo, Elise
EDIT: Added Ryoma to the known elemental users list. The pillars of light that Robin does is also most likely his C6.